Cosmic strings accumulate like dark matter in the potentials of gravitationally bound structures in the Universe.
Thus, missions targeting the bulge of our galaxy are of interest for searches of cosmic loops. WFIRST observations
of the bulge will be sensitive to string tensions in the range of 10-15 - 10-12. We evaluate WFIRST's efficiency
for detecting cosmic string microlensing, assessing the effect of various detection criteria on the rate of false
dismissals and false detections. Our method is to generate data representative of string loop properties and simulate
the predicted WFIRST observations. We suggest strategies that optimize prospects for detection and measuring string
loop tensions and parameters. Detecting cosmic strings WFIRST would allow us to have a better understanding of the physical
laws that governed the early universe, as well as a better understanding of the inflation era and how topological defects were created.
Download a copy of my poster for the 235th AAS Meeting here.
Find the link to the abstract in NASA ADS here.
Introduction
Superstrings are one-dimensional structures created near the end of the inflation era. They interact only gravitationally, which allows
us to study them via gravitational microlensing. Intercommutation between the strings can result in cosmic loops, which radiate
their length and rest mass in the way of gravitational waves. The size of these loops scales with the size of the cosmic horizon, thus smaller
loops were formed in the early stages of the universe. Moreover, the expansion of the universe slows down the motion of the loops
and makes them behave like cold dark matter, which makes them more likely to be found in the potentials of galaxies. The motivation for the search of superstrings is that
they can yield information about the physical laws that governed the early universe, specifically the inflation epoch. Furthermore, there are several intruments being developed
that could possibly be sensitive to the microlensing scales of cosmic strings. One of the leading missions that could potentialy accomplish this is WFIRST. For past work on cosmic string
microlensing refer to Chernoff et al. 2007 and Chernoff et al. 2019.
WFIRST
The Wide Field Infrared Space Telescope (WFIRST) is set to launch in the mid-2020s and it is designed to study a wide
range of cosmological topics ranging from dark energy to exoplanets. The microlensing survey will observe ten contiguous
fields between galactic longitudes -0.5 and 1.8 and latitudes of -1 and -2.2. There will be six 72-day seasons that will
result in a total survey time of 0.98 years. WFIRST will be sensitive to string tensions in the order of 10-15 to 10-12.
Cosmic String Microlensing
The string's positive energy and negative pressure leave spacetime flat. The presence of the string creates a conical geometry and deficit angle ΔΘ= 8πμG/c2, where μ is the string tension, G is Newton's
constant and c is the speed of light.
When the observer, source and string are aligned, the photons of the source have multiple paths to travel. These two paths are label by solid lines in Figure 1. The observer sees two images separated by the angle δφ = ΔΘ(1-d/D), where d is the distance from the observer to the
string and D the distance from the observer to the source.
Fig. 1: Figure obtained from Chernoff et al. (2019) .
Figure 2 illustrates how a microlensing signal is produced from a moving, oscillating cosmic string loop. In the first two panels, the loop is passing in front of a source (red dot), oscillating many times during the process, which creates
multiple signals. These signals are represented in the rightmost panel, where each vertical bar represents an instance in which we would measure twice the flux from a source due to the string crossing the line-of-sight.
A microlensing event creates a digital signal in the light curve with a magnification close to 2, which differentiates it from any lensing signal caused by a different source.
Fig. 2: Figure obtained from Chernoff et al. (2019) .
METHODS
A total of two templates and an algorithm were developed in order to assess WFIRST's efficiency at detecting cosmic string microlensing. The observing template
is a representation of the observing timeline of the microlensing survey. It was constructed by taking a careful look at the mission manuals and identifying the key parameters of interest, such as the time of observation,
cadence between oberving fields, field of view and filters.
The next step consisted of constructing a microlensing event template that would vary every time the code is run. First, we realize values for different parameters from probability distributions depending on the
nature of the parameter (gaussian distribution, uniform distribution, etc.). Once these parameters have been determined, the different timescales that construct the template (lensing time, loop crossing time and
loop oscillating time) can be determined. The goal is that in every run, these parameters will be changed and thus we can calculate the missions efficiency with many random microlensing events. Figure 3
illustrates a pseudo microlensing event and accurately describes the different times that we are interested in. The event time (te) is the period during which the source is magnified, the oscillating time (tosc) is the period of oscillations, the crossing time (tcross)is time the string takes to cross the line-of-sight
and Nrep is number of times the source will be magnified by the same loop. The y-axis in the amplitude (flux) of the signal, which is shown to double when the string is aligned with the source
and observer.
Fig. 3: Figure obtained from Prof. Chernoff.
The last part of the project consited of developing a conditional algorithm, named "Zipper Algorithm", that compares the two templates simultaneously and yields the overlaps. These overlaps
are values between 0 and 2, the latter indicating there has been a microlensing event and we have detected twice the flux. Figure 5 illustrates the nature of this algorithm.
Fig. 4: Visual representation of the "Zipper Algorithm". The blue windows represent observing periods and the red
windows the event time for each microlensing signal.
Future Work
Instrumental error for WFIRST depends on the magnitude of the source that is being magnified, thus a more accurate model for the distribution of stellar magnitudes in the bulge needs to be used. Furthermore,
thresholds for characterizing what we consider a microlensing event or not in order to minimize the amount of false dismissals and false detections need to be determined.
Acknowledgments
This material is based upon work supported by the National Science Foundation under grant No. AST-1659264.
The development of this research project was possible due to the Department of Astronomy at Cornell University.
The work was also partially funded by the Dr. Donald W. Schuerman Memorial Fund Award from the University of Florida Astronomy Department.
